Finding pdfs related to the standard normal

Given a random variable Z is standard normal. I am trying to find the pdfs for the abs(Z) and Z^2.

I thought to start the abs(Z) by splitting the CDF of Z into two separate integrals and adding them (One for when Z>0 and one for when Z<0). Then I would take the derivative to get back to a pdf, but i am struggling to choose the limits of integration.